Page 118 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch09 Elementary Physical Chemistry

Applications of Quantum Theory 103

no two electrons can have the same four quantum numbers. If two electrons
are in the same orbital, they will have the same quantum numbers n, l,
and m l but must have different spin quantum numbers (i.e. opposite spin
quantum numbers). Obviously, no other electron can be put in this orbital.
If another electron is put in this orbital, two spin quantum numbers will
have to be equal, and this violates Pauli’s Principle.
Pauli’s Principle forms the basis for the Aufbau (Built-up) Principle,
and is essential for determining atomic structures by applying Hund’s
Rule. Hund’s rule states that “the most stable configuration favors unpaired
electrons among degenerate orbitals”.
Periodic Trends
Recall from freshman chemistry that the atomic radius increases down the
group in the periodic table and decreases across the period. On the other
hand, the ionization energy decreases down the group and increases across
the period. This can be explained by observing that the orbital “radius”
progresses as follows: 1s< 2s, 2p< 3s, 3p< 4s, 4p...

9.11. Selection Rules for Spectroscopic Transitions
These rules require that
∆l =1 or −1 (also that ∆m l =0, +1 or −1) (9.11a)

and that
∆n = unrestricted (9.11b)

enabling one to determine which transitions are allowed and which are
forbidden.
The reason behind these rules has to do with the spin of a photon,
which is one. Thus, if an atomic electron jumps from a p orbital to an s
orbital there is a loss of one unit of angular momentum. The emitted photon
carries off this unit, and angular momentum is conserved.